Probability Propagation Over Factor Graphs

1. A method for implementing propagation of probability distributions of random variables over a factor graph, the method comprising: providing a spiking neural network, having variable nodes interconnected with factor nodes, corresponding to the factor graph, wherein each of said nodes comprises a set of neurons configured to implement computational functionality of that node; generating, for each of a set of the random variables, at least one spike signal in which the probability of a possible value of that variable is encoded via the occurrence of spikes in the spike signal; and supplying the spike signals for said set of random variables as inputs to the neural network at respective variable nodes; whereby said probability distributions are propagated via the occurrence of spikes in signals propagated through the neural network.

2. The method as claimed in claim 1 including generating each said spike signal such that said probability is encoded via at least one of the rate of occurrence and the time of occurrence of spikes in the spike signal.

3. The method as claimed in claim 2 wherein the neurons of said nodes are configured such that said probability distributions are propagated via at least one of the rate of occurrence and the time of occurrence of spikes in signals propagated through the neural network.

4. The method as claimed in claim 3 including generating each said spike signal such that said probability is encoded via the rate of occurrence of spikes in the spike signal, wherein the neurons of said nodes are configured such that said probability distributions are propagated via the rate of occurrence of spikes in signals propagated through the neural network.

5. The method as claimed in claim 1 wherein the random variables are binary variables, the method including generating, for each random variable of said set, a single spike signal encoding the probability of a predetermined one of the binary values of the variable.

6. The method as claimed in claim 1 wherein the random variables are multivalued variables, the method including generating, for each possible value of each random variable of said set, a spike signal encoding the probability of that value of the variable.

7. A method for detecting error-correction codewords, in a signal sampled at a channel output, by propagating probability distributions of codeword symbols corresponding to respective signal samples over a factor graph, the method comprising: providing a spiking neural network, having variable nodes interconnected with factor nodes, corresponding to a bipartite factor graph defined by a decoding algorithm of the error-correction code, wherein each of said nodes comprises a set of neurons configured to implement computational functionality of that node; generating, for each signal sample corresponding to a symbol of a codeword, at least one spike signal in which the probability of a possible symbol value for that sample is encoded via the occurrence of spikes in the spike signal; and supplying the spike signals corresponding to the symbols of a codeword as inputs to the neural network at respective variable nodes; whereby said probability distributions are propagated via the occurrence of spikes in signals propagated through the neural network and said variable nodes output estimated symbol values for the codeword after propagation.

8. The method as claimed in claim 7 including generating each said spike signal such that said probability is encoded via at least one of the rate of occurrence and the time of occurrence of spikes in the spike signal.

9. The method as claimed in claim 8 wherein the neurons of said nodes are configured such that said probability distributions are propagated via at least one of the rate of occurrence and the time of occurrence of spikes in signals propagated through the neural network.

10. The method as claimed in claim 9 including generating each said spike signal such that said probability is encoded via the rate of occurrence of spikes in the spike signal, wherein the neurons of said nodes are configured such that said probability distributions are propagated via the rate of occurrence of spikes in signals propagated through the neural network.

11. The method as claimed in claim 7 wherein the codeword symbols are binary symbols, the method including generating, for each signal sample, a single spike signal encoding the probability of a predetermined one of the binary symbol values.

12. The method as claimed in claim 7 wherein the codeword symbols are multivalued symbols, the method including generating, for each possible symbol value of each signal sample, a spike signal encoding the probability of that symbol value for the sample.

13. An apparatus for implementing propagation of probability distributions of random variables over a factor graph, the apparatus comprising: a spiking neural network, having variable nodes interconnected with factor nodes, corresponding to the factor graph, wherein each of said nodes comprises a set of neurons configured to implement computational functionality of that node; and a spike signal generator adapted to generate, for each of a set of the random variables, at least one spike signal in which the probability of a possible value of that variable is encoded via the occurrence of spikes in the spike signal, and to supply the spike signals for said set of random variables as inputs to the neural network at respective variable nodes; wherein said probability distributions are propagated via the occurrence of spikes in signals propagated through the neural network.

14. The apparatus as claimed in claim 13 wherein the spike signal generator is adapted to generate each said spike signal such that said probability is encoded via at least one of the rate of occurrence and the time of occurrence of spikes in the spike signal.

15. The apparatus as claimed in claim 14 wherein the neurons of said nodes are configured such that said probability distributions are propagated via at least one of the rate of occurrence and the time of occurrence of spikes in signals propagated through the neural network.

16. The apparatus as claimed in claim 15 wherein the spike signal generator is adapted to generate each said spike signal such that said probability is encoded via the rate of occurrence of spikes in the spike signal, and wherein the neurons of said nodes are configured such that said probability distributions are propagated via the rate of occurrence of spikes in signals propagated through the neural network.

17. The apparatus as claimed in claim 13 wherein the random variables are binary variables, and wherein the spike signal generator is adapted to generate, for each random variable of said set, a single spike signal encoding the probability of a predetermined one of the binary values of the variable.

18. The apparatus as claimed in claim 13 wherein the random variables are multivalued variables, and wherein the spike signal generator is adapted to generate, for each possible value of each random variable of said set, a spike signal encoding the probability of that value of the variable.

19. An apparatus for detecting error-correction codewords, in a signal sampled at a channel output, by propagating probability distributions of codeword symbols corresponding to respective signal samples over a factor graph, the apparatus comprising: a spiking neural network, having variable nodes interconnected with factor nodes, corresponding to a bipartite factor graph defined by a decoding algorithm of the error-correction code, wherein each of said nodes comprises a set of neurons configured to implement computational functionality of that node; and a spike signal generator adapted to generate, for each signal sample corresponding to a symbol of a codeword, at least one spike signal in which the probability of a possible symbol value for that sample is encoded via the occurrence of spikes in the spike signal; wherein said probability distributions are propagated via the occurrence of spikes in signals propagated through the neural network and said variable nodes are adapted to output estimated symbol values for the codeword after propagation.

20. The apparatus as claimed in claim 19 wherein each neuron of a variable node is adapted to implement a majority rule function.

21. The apparatus as claimed in claim 19 wherein each factor node comprises neurons configured to implement an XOR function.

22. The apparatus as claimed in claim 19 wherein the spike signal generator is adapted to generate each said spike signal such that said probability is encoded via at least one of the rate of occurrence and the time of occurrence of spikes in the spike signal.

23. The apparatus as claimed in claim 22 wherein the neurons of said nodes are configured such that said probability distributions are propagated via at least one of the rate of occurrence and the time of occurrence of spikes in signals propagated through the neural network.

24. The apparatus as claimed in claim 23 wherein: the spike signal generator is adapted to generate each said spike signal such that said probability is encoded via the rate of occurrence of spikes in the spike signal; and the neurons of said nodes are configured such that said probability distributions are propagated via the rate of occurrence of spikes in signals propagated through the neural network.

25. A computer program product comprising a computer readable storage medium having program instructions embodied therein, the program instructions being executable by processing apparatus to cause the processing apparatus to perform propagation of probability distributions of random variables over a factor graph by: implementing a spiking neural network, having variable nodes interconnected with factor nodes, corresponding to the factor graph, wherein each of said nodes comprises a set of neurons configured to implement computational functionality of that node; generating, for each of a set of the random variables, at least one spike signal in which the probability of a possible value of that variable is encoded via the occurrence of spikes in the spike signal; and supplying the spike signals for said set of random variables as inputs to the neural network at respective variable nodes; whereby said probability distributions are propagated via the occurrence of spikes in signals propagated through the neural network.